On spontaneous breaking of conformal symmetry by probe flavour D-branes

Journal of High Energy Physics, Mar 2014

We explore the possibilities of breaking conformal symmetry spontaneously by introducing flavour branes into conformal holographic backgrounds in the probe limit. A prototype model of such a mechanism is based on placing \( D7-\overline{D}7 \) configuration in the Klebanov-Witten conifold based model. In this paper we generalize this model. We conjecture on the required topology of the backgrounds and the corresponding probe brane embeddings. We identify several models that obey these requirements and admit spontaneous breaking of conformal invariance. These include type IIB conifold based examples, dual to defect field theories based on the conifold, and type IIA constructions based on the ABJM model. We identify the dilaton, the corresponding Goldstone boson, discuss its effective action and address the “a-term”. We briefly discuss the relevance of these models to the pseudo dilaton.

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On spontaneous breaking of conformal symmetry by probe flavour D-branes

Omer Ben-Ami 1 Stanislav Kuperstein 0 Jacob Sonnenschein 1 0 Institut de Physique Theorique , CEA Saclay, CNRS URA 2306, F-91191 Gif-sur-Yvette, France 1 Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel-Aviv University , Ramat-Aviv 69978, Israel We explore the possibilities of breaking conformal symmetry spontaneously by introducing flavour branes into conformal holographic backgrounds in the probe limit. A prototype model of such a mechanism is based on placing D7-D 7 configuration in the Klebanov-Witten conifold based model. In this paper we generalize this model. We conjecture on the required topology of the backgrounds and the corresponding probe brane embeddings. We identify several models that obey these requirements and admit spontaneous breaking of conformal invariance. These include type IIB conifold based examples, dual to defect field theories based on the conifold, and type IIA constructions based on the ABJM model. We identify the dilaton, the corresponding Goldstone boson, discuss its effective action and address the a-term. We briefly discuss the relevance of these models to the pseudo dilaton. 1 Introduction Mass and VEV deformation by probe D7-Branes More U-shape examples 3.1 D5 probe wrapping AdS3 S3 in AdS5 T 1,1 3.2 D5 probe wrapping AdS4 S2 in AdS5 T 1,1 3.3 D3 probe wrapping AdS2 S2 in AdS5 T 1,1 3.4 D4 probe wrapping AdS3 CP1 in AdS4 CP3 4 The dilaton Models with a pseudo-dilaton 6 Summary and open questions 1 Introduction Known examples of spontaneous conformal symmetry breaking are scarce. Although classically it may not be hard to find conformal invariant (interacting) field theories, it becomes a highly non-trivial task at the quantum level. This is due to the fact that one has to introduce a scale in order to regularize the theory. This scale can explicitly break the symmetry by telling us that marginal operators are not exactly marginal (i.e. QCDs function) or, rather miraculously, tell us that they are (the perturbative Banks-Zaks [1] interacting fixed point). Finding such conformal theories is the first step. The second is to break the symmetry spontaneously. This means that the deformation of the interacting conformal field theory, initiating an RG-flow, should be a VEV deformation. VEV deformations with flat directions are especially hard to come by in conformal theories where Mexican hat models are, of course, out of the question. They do come by, however, in supersymmetric conformal theories where flat directions are present also at the quantum level. The prime example being N = 4 SUSY with an RG flow from SU(N ) to SU(N 1), initiated by giving a VEV to one of the scalars. Integrating out the massive fields, the theory flows from one fixed point to the other. Although not necessarily perturbative, in these models only operators that already appear in the Lagrangian acquire a VEV. There is another well known possibility of breaking a symmetry spontaneously by strong coupling effects. This is usually also referred to as dynamical symmetry breaking. This is what happens in nature in chiral symmetry breaking where the quark condensate is the order parameter for the symmetry breaking. Strongly coupled conformal theories can in principle display the same behavior, thus breaking conformal symmetry spontaneously. Generally speaking, there is no reason why there should be a flat potential for the scalar(s) in the theory (whether they are perturbative and already appear in the UV Lagrangian or a mesonic like operator). Supersymmetry, however, provides a mechanism which preservers the flat directions and allows for the scalar to receive an arbitrary VEV thus breaking the symmetry spontaneously. The models we explore break supersymmetry but still allow for the conformal symmetry to be broken spontaneously. We suspect that this is an artifact of our probe approximation and all corrections to the potential should appear once backreaction is included. Our main motivation is to search for holographic models that admit spontaneous breaking of conformal invariance in a certain type of holographic models. In general, spontaneous breaking of conformal symmetry in a holographic gravity setup can be done either by analysing holographic gravitational background with (or without) additional bulk fields or by embedding Nf flavour D-branes in such backgrounds. Examples of the former approach can be found in [2, 3] where domain wall geometries in arbitrary number of dimensions interpolating between two AdS spaces, were analysed. In this paper we follow solely the latter, D-brane embedding approach. Moreover, we will consider only the probe limit, where one can ignore the backreaction of the embedded D-branes on the geometry. This is easily achieved by taking the Nf Nc limit and in our discussion we will restrict ourself only to the Nf = 1 case. We use the terminology flavour branes for branes which reach the UV boundary (unlike g (...truncated)


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Omer Ben-Ami, Stanislav Kuperstein, Jacob Sonnenschein. On spontaneous breaking of conformal symmetry by probe flavour D-branes, Journal of High Energy Physics, 2014, pp. 45, Volume 2014, Issue 3, DOI: 10.1007/JHEP03(2014)045